The incident, which took place in Restalrig Circus on Friday 24th January, saw emergency services called to the home of the woman - who was later named as Margaret Grant - at approximately 6.50 pm after there were reports of a disturbance at the property.
• READ MORE: Edinburgh pensioner Margaret Grant, 79, died after attack by robber who knew herParamedics then took 79-year-old Margaret to the Edinburgh Royal Infirmary, where Police Scotland later confirmed that she died.
Detectives urged any witnesses who may have had information to come forward, and also called on the man behind the attack to hand himself in.
At the time, the local community spoke of their shock at the incident, one neighbour said: "I came home from work and there were police everywhere and the entrance to our flat was cordoned off. It was a bit worrying because my wife and children were at home when all this was happening.”
Neighbours Robina Burke, 81, and Elaine Burke, 57, described Ms Grant was a "beautiful soul" and said she "wouldn't hurt a fly".
The police stated that a man is now due to appear at Edinburgh Sheriff Court on Wednesday 19th February.